Answer:
[tex]\huge\boxed{x = 11,\ y = 3}}[/tex]
Step-by-step explanation:
In order to find the value of x and y in this, we have to note a couple of angle relationships.
We know that angles [tex]13x-19[/tex] and [tex]9x+25[/tex] are the same because they are corresponding angles. This means that when a line intersects two parallel lines, the angles formed are congruent to the second line.
This means both expressions for the line will be equal to each other:
[tex]13x-19 = 9x+25[/tex]
We can now solve for x.
Add 19 to both sides:
[tex]13x = 9x+44[/tex]
Subtract 9x from both sides:
[tex]4x=44[/tex]
Divide both sides by 4:
[tex]x=11[/tex]
Now that we know that x = 11, we can use another angle relationship to find y.
We know that [tex]13x-19[/tex] and [tex]17y+5[/tex] are supplementary angles. This means their angle measurements add up to 180°.
Since we know the value of x, we can find the measure of the angle [tex]13x-19[/tex].
[tex]13(11) -19\\\\143-19\\\\124[/tex]
So the [tex]13x-19[/tex] angle is equal to 124 degrees. Since this and [tex]17y+5[/tex] are supplementary, that means [tex]17y+5[/tex] must be equal to [tex]180-124=56[/tex] degrees.
[tex]17y+5=56[/tex]
Subtract 5 from both sides:
[tex]17y=51[/tex]
Divide both sides by 17:
[tex]y=3[/tex]
So, x = 11 and y = 3.
Hope this helped!
